Distribution of catecholamine fibers in the cochlear nucleus of

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THE JOURNAL OF COMPARATIVE NEUROLOGY 269523-534 (1988)
Distribution of Catecholamine Fibers in
the Cochlear Nucleus of
Horseshoe Bats and Mustache Bats
M. KOSSL, M. VATER, AND H. SCHWEIZER
Zoologisches Institut der Universitat Munchen, 8000 Munchen 2, Federal Republic of
Germany
ABSTRACT
The glyoxylic-acid-induced fluorescence technique was applied to demonstrate patterns of catecholaminergic innervation within the auditory
brainstem of echolocating bats and the house mouse. In the cochlear nucleus
of the rufous horseshoe bat (Rhinolophus rouxi) and the mustache bat (Pteronotus pamellii), species-specific catecholaminergic innervation patterns are
found that contrast with the relatively homogeneous innervation in the
rodent.
In both bats the subnuclei of the cochlear nucleus receive a differentially
dense supply of catecholaminergic fibers, and within the subnuclei, the
catecholamine innervation densities can be correlated with the tonotopic
frequency representation. The areas devoted to the high-frequency echolocation calls are less densely innervated than those regions which are responsive to lower frequencies.
Apart from this common scheme, there are noteworthy distinctions
between the two bats which correlate with specialized cytoarchitectural
features of the cochlear nucleus. The marginal cell group, located medially
to the anteroventral cochlear nucleus of Pteronotus, receives the densest
supply of catecholaminergic fibers of all auditory nuclei. This plexus is
formed by a morphologically distinct population of catecholaminergic fibers.
Key words: histofluorescence, auditory system, echolocation
Sensory processing is known to be modulated by catecholamines (CAI (Foote et al., '75; Pettigrew and Kasamatsu,
'78; Rogawski and Aghajanian, '80; Waterhouse et al., '80).
For the auditory system, Foote et al. ('75) report a n improvement of the signal-to-noise ratio of cortical auditory
neurons during noradrenaline (NA) injection. Noradrenergic input appears to influence auditory neuronal responses already at the cochlear nucleus (CN), the first
central synaptic station of the ascending auditory pathway.
During electrical stimulation of the locus ceruleus (LC), the
site of origin of noradrenergic fibers (Levitt and Moore, '79),
the activity of auditory neurons in the CN is inhibited
(Chikamori et al., '80). A behavioral study of Pickles ('76)
showed that local application of NA onto the surface of the
CN increased both absolute and masked tone thresholds.
The anatomical basis for these actions is the relatively
dense innervation of the CN by catecholaminergic fibers
(Kromer and Moore, '76: rat).
The present study investigates and compares the distribution of catecholaminergic fibers in the CN of two bat
species and the house mouse. The CN of echolocating bats
1988 ALAN R. LISS. INC.
represents a promising model for studying the mode and
degree of catecholaminergic influence on the peripheral
auditory system. In horseshoe bats and mustache bats parts
of the CN are hypertrophied, and the functional organization of the CN reveals adaptations for processing the echolocation calls (Suga et al., '75); Neuweiler and Vater, '77;
Schweizer, '81; Zook and Casseday, '82; Feng and Vater,
'85). Both bats use multiharmonic orientation calls consisting of a long constant frequency (CF) component followed
by a frequency-modulated component, and the auditory system is sharply tuned to the CF frequency of the second
harmonic (Pollak et al., '72; Suga et al., '75; Neuweiler et
al., '80). Despite this convergent evolution, the cytoarchitectural substructure of the CN shows some remarkably different features. The dorsal CN (DCN) is divided into a
laminated and nonlaminated part in Rhinolophus
(Schweizer, '78, '81; Feng and Vater, '85), whereas in Pteronotus it is only weakly laminated as a whole (Zook and
Casseday, '82). Significantly, the CN of Pteronotus contains
Accepted October 13, 1987.
M. KOSSL ET AL.
524
a group of large multipolar neurons, the marginal cells
(Zook and Casseday, '82),which is not found in other mammals. In both species the tonotopic arrangement in the
three subnuclei is known and found to be biased toward an
overrepresentation of the frequency range of the CF frequency of the dominant second harmonic of the orientation
call (Feng and Vater, '85; Kossl, '87). With this background,
the question can be addressed of whether the innervation
by a modulatory neuronal system like the catecholaminergic system is related to cytoarchitectural areas involved in
processing of biologically relevant frequency information.
We report that both the degree and pattern of the catecholaminergic innervation in the CN of bats differ significantly
from the house mouse and are related to the frequency
representation. Furthermore, the marginal cells of Ptere
notus receive the densest supply of Ca fibers within the
auditory system.
MATERIALS AND METHODS
Four individuals of Rhinolophus rouxi from Sri Lanka,
four Pteronotus parnellii from Jamaica, and three house
mice (Mus musculus) were used. The animals were decapitated under deep nembutal anaesthesia (5 mgl100 g body
weight). The brains were quickly removed and then processed according to a slightly modified protocol of de la
A bbreuiatioias
auditory nerve
anteroventral cochlear nucleus
anterior part of AV
posterior part of AV
catecholamine
constant-frequency component of echolocation calls
CF
cochlear nucleus
CN
dopamine
DA
dorsal acoustic stria
das
dorsal cochlear nucleus
DCN
dorsal part of DCN
DCd
ventral part of DCN
DCV
dorsal tegmental nucleus (van Gudden)
dt
facial nerve
f
facial nucleus
fn
granular cells
intermediate acoustic stria
Z S
inferior colliculus
IC
inferior cerebellar peduncle
FP
inferior olivary complex
10
locus ceruleus
LC
LNTB lateral nucleus of the trapezoid body
lateral superior olivary nucleus
LSO
lateral tegmentum
LT
marginal cell group
MA
lateral part of MA
MA1
MAm medial part of MA
middle cerebellar peduncle
mcP
MNTB medial nucleus of the trapezoid body
medial superior olivary nucleus
MSO
noradrenaline
NA
posteroventral cochlear nucleus
PV
dorsal part of PV
PVd
ventral part of PV
PVV
lateral part of PV
PV1
medial part of PV
PVm
rm
raphe magnus
superior cerebellar peduncle
SCP
spinal tract of trigeminal nerve
st
trapezoid body
tb
motor nucleus of the trigeminal nerve
tm
principal sensory nucleus of the trigeminal nerve
ts
VNTB ventral nucleus of the trapezoid body
vestibular ganglion
vg
an
AV
AVa
$2
Torre and Surgeon ('76) and de la Torre ('80). Brain tissue
slabs 5-10 mm thick containing the brainstem and the
cerebellum were cut and immediately placed onto the object-holder of the precooled cryostat that maintained a temperature of -28" to -30°C. Sections 30 pm thick were cut,
attached to a glass slide, and immediately dipped three
times into the glyoxylic acid solution (1%glyoxylic acid
monohydrate, 6.8% sucrose). The sections were air dried,
covered with paraffin oil, and then kept for 3.5 minutes in
an oven prewarmed to 94-97°C. Coverslips were applied
and the slides were ready for examination with a ReichertJung epifluorescence microscope (excitation filter 390-450
nm, barrier filter 475 nm). With this method NA and dopamine (DA) were indistinguishable since they emit similar
blueigreen fluorescence, but both were easily differentiated
from the yellow, fast-fading serotonin reaction product.
Since the cutting plane cannot be accurately controlled
with this procedure, the transverse sections of different
brains are oriented in slightly different angles (see Fig. 9).
Transverse sections were cut in a plane roughly perpendicular to the dorsal surface of the cortex, and the dorsoventral
axis in the figures refers to this plane. Since the brainstem
of bats is flexed in relation to the cortex surface, the anterior part of the anteroventral CN is shifted dorsally and the
DCN ventrally. This is due to the cutting plane and does
not reflect a principle difference to other mammals. To
verify CA distribution differences found on different transverse sections, additional brains were cut parasagittally.
The sections were analyzed at 250 times and 1,000 times
magnification and representative drawings were made of
all detectable fibers and terminals with a camera lucida.
After examination for fluorescence the sections were stained
with cresyl violet for cytoarchitectural analysis. Cytoarchitectural borderlines were defined by superimposing the
stained sections and the drawings, using brain outlines,
small holes, and blood vessels as reference. Additional slices
from different brains were processed for acetylcholinesterase with a modified Koelle-Friedenwald thiocholine method
according to Hardy et al. ('76). The cytoarchitectural division of the CN is on the basis of the work of Zook and
Casseday ('82) for Pteronotus and Feng and Vater ('85) for
Rhinolophus. For the house mouse the nomenclature of
Willard and Ryugo ('83)was used. On the basis of the
pattern of CA innervation and results on the auditory frequency representation in the CN of Pteronotus (Kossl, '871,
the marginal cell group was further divided into a lateral
and medial part.
RESULTS
Catecholaminergic fibers are readily detected by their
intense bluelgreen fluorescence. Fluorescent fibers in the
CN are approximately 0.5-2 pm in diameter (Figs. 2,6) and
show characteristic varicosities separated by intervaricose
segments. The varicosities represent the typical terminal
specializations of CA fibers as sites of transmitter release
(Moore and Card, '84).
The fiber distribution within the CN is species specific.
In the house mouse all the subnuclei of the CN receive a
rather homogeneous innervation by CA fibers (Fig. l),and
the fiber distribution is similar to that in the rat (Kromer
and Moore, '76). There are only minor variations in density.
In the posteroventral CN (PV) the density is slightly higher
than in the anteroventral CN (AV), and within the DCN,
the molecular layer receives a low fiber supply. In contrast,
both bats show clear regional differences in the CA inner-
525
CATECHOLAMINE INNERVATION OF BAT COCHLEAR NUCLEUS
Mus musculus
d
das
L
m
Fig. 1. Camera lucida drawings of catecholaminergic fibers (glyoxylic-acid-induced histofluorescence) in the
cochlear nucleus of the house mouse (transverse sections). The fibers are relatively homogeneously distributed
with a slightly denser innervation in the PV. They enter the CN with the das and between the mcp and st. As in
Figures 3 and 4; section numbers starting from the most caudal CN section are given in parentheses.
vation pattern of the CN. Moreover, the areas of highest
fiber density are different between the two bat species (Figs.
2-4).
In Rhinolophus the DCN is most heavily innervated with
CA fibers (Figs. 2, 3, 5). This subnucleus is composed of a
laminated ventral part (DCv), similar to the DCN of other
nonprimate mammals, and a dorsal part (DCd) lacking
lamination (Feng and Vater, '85). The ventral DCN, where
low frequencies are processed, exhibits a particularly prominent network of CA fibers (Fig. 2a). This plexus is densest
at the location of granular cells, which form a caplike structure extending from the DCN to the laterocaudal AV and
PV (Figs. 3, 5). The dorsal DCN is less densely innervated
than the ventral DCN (see Fig. 5). The dense innervation
of the granular cells in Rhinolophus is in clear contrast to
the house mouse, where granular cell areas are innervated
by fibers of similar density as in the rest of the CN (Fig. 1).
The ventral CN of Rhinolophus has a significantly lower
innervation density than the DCN. In particular the caudal
part of the AV, where high frequencies are represented
(Feng and Vater, '85), is only sparsely innervated. The
innervation density increases toward more rostral sections
of the AV, where low frequencies are represented (Feng and
Vater, '85). This is especially evident in the sagittal series
of Figure 5 . Judging from cytoarchitecture the AV can be
separated into an anterior part (AVa) with densely packed
small spherical cells, and a posterior part (AVp) of lower
cell density, which additionally contains large multipolar
or globular cells (Feng and Vater, '85). This cytoarchitec-
tural separation does not exactly match the CA innervation
pattern since the rostral parts of both anterior and posterior
AV are more densely innervated, but in general the anterior AV has higher CA density.
The PV is divided into a dorsal part (PVd) of low cell
density containing large multipolar or stellate cells and a
ventral part (PVv) which is densely populated by small
cells. The CA innervation is sparse throughout PV. A
slightly higher fiber density in the rostral and ventral parts
of the PV roughly coincides with the PVd/pVv distinction.
The cytoarchitecture and the CA innervation pattern of
the CN of Pteronotus are in some aspects clearly different
from Rhinolophus (Figs. 2 , 4 , 5).
The DCN of Pteronotus is not divided into two cytoarchitectural regions as in Rhinolophus, and the degree of lamination is low (Zook and Casseday, '82). The CA innervation
density is comparable to the dorsal DCN of Rhinolophus
and is generally higher than in the adjacent AV or PV but
lower than in the ventral DCN of Rhinolophus. The granular cell cap also receives a dense CA innervation but is in
its extension not as prominent as in Rhinolophus. The
innervation of the AV is higher in rostral than in caudal
regions and thus comparable to Rhinolophus. In the PV the
CA innervation is less homogeneous than in Rhinolophus
since the medial PV (PVm, homologous to the Rhinolophus
PVv) clearly receives a denser CA fiber supply than the
lateral PV (PV1, homologous to PVd) (Figs. 4,5).
The highest CA innervation density of the whole CN
complex of Pteronotus is found in the marginal cell (MA)
Fig. 2. Photomicrographs of catecholaminergic fibers in the cochlear nucleus of the two bat species. a: DCN
and PV of Rhinolophus. Note that the DCN has a much denser CA innervation than the PV. b: MA cells and AV
of Pteronatus. Note the very dense innervation of the MA cell group and of the ventral part of the AV. Transverse
sections, calibration bar represents 100 pm.
CATECHOLAMINE INNERVATION OF BAT COCHLEAR NUCLEUS
527
Rhinolophus
das
(21)
PVV
d
tI
m
Ia s
Fig. 3. Camera lucida drawings of the catecholaminergic innervation of the cochlear nucleus of Rhinolophus
(transverse sections). Note the areas of densest innervation in the ventral part of DCN (DCv) and the granular
cell cap of AV and PV (gr). The rostral parts of AV and PV also show higher innervation density than the caudal
parts. The fibers enter through the das, ias, and the tb.
area and in the rostral AV (Figs. 2b, 4). The MA group
contains large multipolar cells darkly staining with cresyl
violet and is a species characteristic feature of Pteronotus
(Zook and Casseday, '82). These cells are located either
medially to AV and PV (here defined as medial subdivision
of MA: MAm) or between DCN and PV (lateral subdivision:
MA1). The dense CA fiber network is restricted to the medial MA group and to adjacent parts of the ventral and
rostral AV (both AVa and AVp) (Figs 4,5). The dense fiber
network does not extend into the lateral MA group where
the fiber density is not higher than in the surrounding PV1
and DCN (Figs. 4,5). As demonstrated in Figure 7, which
shows the relation of the CA fibers to Nissl-stained cell
bodies, the medial MA cells are covered by a very dense
carpet of fibers that also fills up the neuropil. The fibers in
this area are even denser than in Rhinolophus DCN (com-
pare Fig. 6a with 6b, Fig. 7) and appear t o be finer (Fig. 6).
They show many varicosities that are on the average
smaller than in the rest of the CN complex of both bats,
and the difference between varicosities and intervaricose
segments is less distinct. Because of the numerous varicosities and the high degree of arborization these fibers most
probably constitute a terminal field and are not fibers of
passage. Such passing fibers are seen in the trapezoid body
and are straighter and thicker and show less varicosities.
The CA fiber network of the medial MA represents the
most densely CA-innervated area of the auditory system.
In addition to the CA innervation the medial group also
receives a rather dense and distinct network of fibers staining positively in acetylcholinesterase histochemistry (Fig.
8).The area of dense acetylcholinesterase stain is restricted
to the medial MA group, does not cover the lateral MA
528
M. KOSSL ET AL.
Pt e ronot us
das
das
PV
ill1
(15)
(23)
(27)
1331
d
b
153)
159)
Fig. 4. Camera lucida drawings of the catecholaminergic innervation of the cochlear nucleus of Pteronotus
(transverse sections). The DCN shows only slightly denser innervation than AV and PV. Maximal CA density is
found in the granular layers (gr)and especially in the medial MA group (MAm) and adjacent ventral AV.
content.
The CA fibers enter the CN complex within different
pathways. One prominent entry is along the dorsal acoustic
stria (das). These fibers presumably supply the DCN and
the granular cells. Additionally there are fibers entering
the AV through the trapezoid body (tb), and also some fibers
enter within the intermediate acoustic stria (ias). Since the
fibers cannot be traced unambiguously over a long distance,
their origin is unclear. In the brainstem catecholaminergic
cell bodies are located in the LC and in the lateral tegmenturn (LT) (Fig. 9), which are probably homologous to rat A5
or A7 cell groups (Moore and Card, '84).In Pteronotus
prominent bundles of CA fibers are travelling ventrally at
the rostrocaudal level of the locus ceruleus and lateral
tegmentum (Fig. 9) and are candidates for supplying the
medial MA terminal field via the trapezoid body.
regionally differentiated pattern of supply. There are differences of innervation density within the subnuclei which
can be correlated with the tonotopic frequency representation. Furthermore, cytoarchitectural differences between
horseshoe bats and mustache bats are reflected by differences in the innervation by CA fibers, which is especially
evident for the MA group of Pteronotus and will be discussed first.
The catecholaminergic innervation of the marginal
cell group
The CA innervation of the CN in Pteronotus shows unusual features correlating with a unique cytoarchitectural
specialization, the MA group. In the CN of rats the CA
innervation seems to be exclusively noradrenergic (Kromer
CATECHOLAMINE INNERVATION OF BAT COCHLEAR NUCLEUS
Rhin
529
Pte
(LI
116)
2 E m
(191
113)
d
I271
Fig. 5. Camera lucida drawings of the distribution of catecholaminergic
fibers (parasagittal sections) in the CN of Rhinolophus (left) and Pteronotus
(right). In Rhinolophus the DCV, granular cells, and rostral AV are most
and Moore, '76; Levitt and Moore, '79). Its origin is most
probably the LC because the biochemically measurable NA
content of the CN disappears after bilateral lesions of the
LC (Levitt and Moore, '79). In the rat the NA fibers of the
LC are characterized by regularly shaped varicosities of
intensive fluorescence and very thin intervaricose segments (Lindvall and Bjorklund, '74a,b; Moore, '78; Levitt
densely innervated. In Pteronotus the medial MA group and the most rostral
AV receive the highest density of supply with CA fibers. Section numbers
starting from the most lateral CN section are given in brackets.
and Moore, '79). Ca fibers of similar morphology innervate
the CN of Rhinolophus and most parts of the CN of Pteronotus and therefore most probably are noradrenergic. A different type of CA fibers is observed in the medial MA
group. These fibers are finer and denser and the varicosities
are smaller (Fig. 6). Their distinct morphology suggests the
possibility that their site of origin is different from the LC.
M. KOSSL ET AL.
530
Fig. 6. Photomicrographs of catecholaminergic fibers in the DCN of Rhinolophus (a)and the medial MA group
of Pteronotus (b). Note that in the medial MA group the fibers are denser and the varicosities are on the average
smaller than in the DCN. Calibration bar represents 10 pm.
The fibers could come either from DA cells of the ventral
and medial tegmentum, which give rise to terminal fibers
of very dense and fine appearance (Lindvall and Bjorklund,
'74a; Bjorklund and Lindvall, '841, or they might originate
in the lateral tegmental NA cells, whose fibers are more
heterogeneous than the LC fibers (Lindvall and Bjorklund,
'74a,b). However, dopaminergic innervation of the CN or
noradrenergic innervation from sources other than the LC
has not been reported in other animals. The precise nature
of the CA innervation of the MAm region is presently being
studied more closely with pharmacological tools. In this
context, it is of considerable interest that both catecholaminergic and acetylcholinergic systems establish dense fiber
networks in the medial MA region. This indicates a functional relationship of the two transmitter systems. Complex
modulatory interactions with acetylcholine are reported
both for DA (Giorguieff et al., '76; Puro, '83; Yeh et al., '841,
and for NA (Loffelholz, '79; Muscholl, '79; Waterhouse et
al., '80).
Relation between CA innervation and frequency
representation
In the CN of the house mouse there is no obvious gradient
of CA fiber innervation: all parts of the subnuclei show
similar fiber densities. Therefore neurons tuned to different
tone frequencies are most probably affected in a similar
degree by the presumed catecholaminergic modulation.
In the anteroventral CN of both Rhinolophus and P t e m
notus, there is a clear increase of CA density from caudal
to rostral. The tonotopic arrangement in the AV is such
that neurons processing similar tone frequencies are arranged in transverse slabs. Slabs of increasing frequencies
are organized in a rostrocaudal direction (Feng and Vater,
'85, for Rhinolophus; Kossl, '87, for Pteronotus). This implies that neurons located rostrally and processing low frequencies receive a denser innervation than the caudally
located high-frequency areas. The regions processing the
dominant second harmonic (Rhinolophus) and second and
CATECHOLAMINE INNERVATION OF BAT COCHLEAR NUCLEUS
531
'7
V
Fig. 7. Camera lucida drawings of the distribution of catecholaminergic layer. Right transverse sections of the AV and the medial MA group of
fibers in relation to the cell bodies superimposed from pictures drawn prior Pteronotus. Despite similar cell density, the medial MA neurons receive
to and after counterstaining the individual section. Left Parasagittal sec- much denser innervation. Calibration bar represents 25 pm.
tions of the DCN of Rhinolophus; most fibers are located in the fusiform cell
third harmonics (Pteronotus) of the echolocation calls (i.e.,
CF frequencies of 78 kHz for Rhinolophus and both 61 and
92 kHz for Pteronotus) underlie less catecholaminergic influence than the areas dealing with the less intense first
harmonic of echolocation calls and with low-frequency communication calls. The same relationship holds true for the
DCN of Rhinolophus where the less densely innervated
dorsal part processes the frequencies of the second harmonic component, whereas the more strongly innervated
ventral part is devoted to lower frequencies. The medial
subdivision of the PV of Pteronotus representing low frequencies is also more densely innervated than the lateral
subdivision, which processes high frequencies. In the PV of
Rhinolophus and the DCN of Pteronotus such gradients are
less obvious or absent. To summarize, in all the subnuclei
of the CN of both bats where there is a significantly inhomogeneous CA innervation, low-frequency regions receive
denser innervation than the high-frequency regions processing the dominant echolocation frequencies. Most interesting is the high innervation density in the medial MA
group in Pteronotus, which contains a frequency represen-
tation biased for frequencies between 24 and 30 kHz (i.e.,
the range of the first harmonic of the echolocation calls;
Kossl, '87).
At present, we can only speculate about the functional
implications of the observed pattern since it remains to be
demonstrated if the presumed modulatory effects of CA
system are inhibitory (Hoffer et al., '71, '73; Siggins et al.,
'71) or more complex and also facilitatory as implied by a
number of reports (Moises et al., '79; Waterhouse et al., '80,
'82; Waterhouse and Woodward, '80). The regional differences in CA supply could imply that signal processing in
the high-frequency areas devoted to the main echolocation
frequencies is rather stereotyped and less susceptibleto CA
modulation.
The dense CA innervation of the low-frequency range
might nevertheless be important for echolocation more indirectly by enabling the animal to focus on specific features
of the acoustic signals:
(1)If the Ca modulation of the CN were mostly inhibitory
as in other species (Pickles, '76; Chikamori et al., '80), its
M. KOSSL ET AL.
532
Fig. 8. Photomicrograph of a n acetylcholinesterase-stained section of the CN of Pteronotus. Note that the
staining is distinctly restricted to the medial MA group. Calibration bar represents 100 pm.
activity would lead to a selective inhibition of the low
frequencies, possibly improving detection of the high-frequency echolocation sounds in noise.
(2) In the central auditory system of Pteronotus the weak
first harmonic (24-30 kHz) of the multiharmonic calls is an
necessary trigger for delay-sensitive neurons. These neurons respond to the high frequencies of the dominant second
or the third harmonic (60 and 90 kHz) only if those have a
certain delay to a first harmonic pulse (Suga et al., ’78,
O’Neill and Suga, ’79, ’82; Suga, ’84). Under the assumption that the first harmonic pulse derives from the emitted
call and the second high-frequency sound from the returning echo, these neurons are able to code the distance be-
tween bat and prey. The distinct CA innervation of the
medial MA group and the rostra1 AV which are responsive
to the frequency range of the first harmonic might play a
role within this functional context. A selective control of
the first harmonic gating mechanism could then be achieved
already at the level of the CN.
ACKNOWLEDGMENTS
This work was supported by the SFB 204 “Gehor.” We
thank G. NeuweiIer and R. Roverud for critically reading
a n earlier version of this manuscript.
533
CATECHOLAMINE INNERVATION OF BAT COCHLEAR NUCLEUS
Pteronotus
Rhinolophus
d
L
Fig. 9. Camera lucida drawings of transverse sections through the brainstem of Rhinolophus (left) and
Pterorzotns (right) showing the location of noradrenergic cell bodies in the locus ceruleus (LC) and in the lateral
tegmentum (LT). Rostrocaudal position is not quite comparable because of differences in the cutting plane. For
further explanation see text.
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